Skip to main content

Electrostatics Interactions in Classical Simulations

  • Protocol
  • First Online:
Book cover Biomolecular Simulations

Part of the book series: Methods in Molecular Biology ((MIMB,volume 924))

Abstract

Electrostatic interactions are crucial for both the accuracy and performance of atomistic biomolecular simulations. In this chapter we review well-established methods and current developments aiming at efficiency and accuracy. Specifically, we review the classical Ewald summations, particle-particle particle-method particle-method Ewald algorithms, multigrid, fast multipole, and local methods. We also highlight some recent developments targeting more accurate, yet classical, representation of the molecular charge distribution.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Alper HE, Levy RM (1989) Computer-simulations of the dielectric-properties of water—studies of the simple point-charge and transferable intermolecular potential models. J Chem Phys 91:1242–1251

    Article  CAS  Google Scholar 

  2. Alper HE, Bassolino D, Stouch TR (1993) Computer-simulation of a phospholipid monolayer-water system—the influence of long-range forces on water-structure and dynamics. J Chem Phys 98:9798–9807

    Article  CAS  Google Scholar 

  3. Alper HE, Bassolino-Klimas D, Stouch TR (1993) The limiting behavior of water hydrating a phospholipid monolayer—a computer simulation study. J Chem Phys 99:5547–5559

    Article  CAS  Google Scholar 

  4. Feller SE, Pastor RW, Rojnuckarin A, Bogusz A, Brooks BR (1996) Effect of electrostatic force truncation on interfacial and transport properties of water. J Phys Chem 100:17011–17020

    Article  CAS  Google Scholar 

  5. Mark P, Nilsson L (2002) Structure and dynamics of liquid water with different long-range interaction truncation and temperature control methods in molecular dynamics simulations. J Comp Chem 23:1211–1219

    Article  CAS  Google Scholar 

  6. Yonetani Y (2006) Liquid water simulation: a critical examination of cutoff length. J Chem Phys 124:204501

    Article  PubMed  CAS  Google Scholar 

  7. Smith PE, Pettitt BM (1991) Peptides in ionic solutions: a comparison of the Ewald and switching function techniques. J Chem Phys 95:8430–8441

    Article  CAS  Google Scholar 

  8. Schreiber H, Steinhauser O (1992) Cutoff size does strongly influence molecular-dynamics results on solvated polypeptides. Biochemistry 31:5856–5860

    Article  PubMed  CAS  Google Scholar 

  9. York DM, Darden TA, Pedersen LG (1993) The effect of long-range electrostatic interactions in simulations of macromolecular crystals—a comparison of the Ewald and truncated list methods. J Chem Phys 99:8345–8348

    Article  CAS  Google Scholar 

  10. York DM, Yang WT, Lee H, Darden T, Pedersen LG (1995) Toward the accurate modeling of DNA—the importance of long-range electrostatics. J Am Chem Soc 117:5001–5002

    Article  CAS  Google Scholar 

  11. Cheatham III TE, Kollman PA (1997) Molecular dynamics simulations highlight structural differences among DNA:DNA, RNA:RNA, and DNA:RNA hybrid duplexes. J Am Chem Soc 119:4805–4825

    Article  CAS  Google Scholar 

  12. Auffinger P, Westhof E (1998) Molecular dynamics simulations of nucleic acids. In: Encyclopedia of computational chemistry. Wiley, New York

    Google Scholar 

  13. Norberg J, Nilsson L (2000) On the truncation of long-range electrostatic interactions in DNA. Biophys J 79:1537–1553

    Article  PubMed  CAS  Google Scholar 

  14. Feller SE, Pastor RW, Rojnuckarin A, Bogusz S, Brooks BR (1996) Effect of electrostatic force truncation on interfacial and transport properties of water. J Phys Chem 100:17011–17020

    Article  CAS  Google Scholar 

  15. Patra M, Karttunen M, Hyvonen MT, Falck E, Vattulainen I (2004) Lipid bilayers driven to a wrong lane in molecular dynamics simulations by subtle changes in long-range electrostatic interactions. J Phys Chem B 108:4485–4494

    Article  CAS  Google Scholar 

  16. Anézo C, de Vries AH, Höltje HD, Tieleman DP (2003) Methodological issues in lipid bilayer simulations. J Phys Chem B 107:9424–9433

    Article  CAS  Google Scholar 

  17. Khelashvili GA, Scott HL (2004) Combined Monte Carlo and molecular dynamics simulation of hydrated 18:0 sphingomyelin-cholesterol lipid bilayers. J Chem Phys 120:9841–9847

    Article  PubMed  CAS  Google Scholar 

  18. Patra M, Hyvonen MT, Falck E, Sabouri-Ghomi M, Vattulainen I, Karttunen M (2007) Long-range interactions and parallel scalability in molecular simulations. Comp Phys Comm 176:14–22

    Article  CAS  Google Scholar 

  19. Karttunen M, Rottler J, Vattulainen I, Sagui C (2008) Computational modeling of membrane bilayers. Elsevier, New York

    Google Scholar 

  20. Heyes DM, Barber M, Clarke JHR (1977) Molecular dynamics computer simulation of surface properties of crystalline potassium chloride. J Chem Soc Faraday Trans 2:1485–1496

    Google Scholar 

  21. Hautman J, Klein ML (1992) An Ewald summation method for planar surfaces and interfaces. Mol Phys 75:379–395

    Article  CAS  Google Scholar 

  22. de Leeuw SW, Perram JW (1979) Electrostatic lattice sums for semi-infinite lattices. Mol Sim 37:1313–1322

    Google Scholar 

  23. Nijboer BRA, de Wette FW (1957) On the calculation of lattice sums. Physica 23:309–321

    Article  CAS  Google Scholar 

  24. Yeh IC, Berkowitz ML (1999) Ewald summation for systems with slab geometry. J Chem Phys 111:3155–3162

    Article  CAS  Google Scholar 

  25. Lekner J (1989) Summation of dipolar fields in simulated liquid-vapor interfaces. Physica A 157:826–838

    Article  CAS  Google Scholar 

  26. Lekner J (1991) Summation of Coulomb fields in computer-simulated disordered systems. Physica A 176:485–498

    Article  Google Scholar 

  27. Lekner J (1998) Coulomb forces and potentials in systems with an orthorhombic unit cell. Mol Sim 20:357

    Article  CAS  Google Scholar 

  28. Sperb R (1994) Extension and simple proof of Lekner’s summation formula for coulomb forces. Mol Sim 13:189–193

    Article  Google Scholar 

  29. Sperb R (1998) An alternative to Ewald sums part I: identities for sums. Mol Sim 20:179–200

    Article  CAS  Google Scholar 

  30. Sperb R (1999) An alternative to Ewald sums, part 2: the Coulomb potential in a periodic system. Mol Sim 22:199–212

    Article  CAS  Google Scholar 

  31. Strebel R, Sperb R (2001) An alternative to Ewald sums. part 3: implementation and results. Mol Sim 27:61–74

    Article  CAS  Google Scholar 

  32. Arnold A, Holm C (2002) A novel method for calculating electrostatic interactions in 2D periodic slab geometries. Chem Phys Lett 354:324–330

    Article  CAS  Google Scholar 

  33. Arnold A, Holm C (2002) MMM2D: a fast and accurate summation method for electrostatic interactions in 2D slab geometries. Comput Phys Comm 148:327–348

    Article  CAS  Google Scholar 

  34. Baker NA (2005) Improving implicit solvent simulations: a Poisson-centric view. Curr Opin Struct Bio 15:137–143

    Article  CAS  Google Scholar 

  35. Stone AJ (1996) The theory of intermolecular forces. Clarendon Press, Oxford

    Google Scholar 

  36. Ewald P (1921) Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann Phys 64:253–287

    Article  Google Scholar 

  37. DeLeeuw SW, Perram JW, Smith ER (1980) Simulation of electrostatic systems in periodic boundary conditions I: lattice sums and dielectric constants. Proc R Soc Lond A373:27–56

    Google Scholar 

  38. Boresch S, Steinhauser O (1997) Presumed versus real artifacts of the Ewald summation technique: the importance of dielectric boundary conditions. Ber Bunseges Phys Chem 101:1019–1029

    Article  CAS  Google Scholar 

  39. Hockney RW, Eastwood JW (1981) Computer simulation using particles. McGraw-Hill, New York

    Google Scholar 

  40. Pollock E, Glosli J (1996) Comments on PPPM, FMM, and the Ewald method for large periodic Coulombic systems. Comp Phys Comm 95:93–110

    Article  CAS  Google Scholar 

  41. Darden TA, York DM, Pedersen LG (1993) Particle mesh Ewald: an N log(N) method for Ewald sums in large systems. J Chem Phys 98:10089–10092

    Article  CAS  Google Scholar 

  42. Essmann U, Perera L, Berkowitz ML, Darden T, Lee H, Pedersen LG (1995) A smooth particle mesh Ewald method. J Chem Phys 103:8577–8593

    Article  CAS  Google Scholar 

  43. York D, Yang W (1994) The fast Fourier Poisson (FFP) method for calculationg Ewald sums. J Chem Phys 101:3298–3300

    Article  CAS  Google Scholar 

  44. Smith ER (1994) Calculating the pressure in simulations using periodic boundary conditions. J Stat Phys 77:449–472

    Article  Google Scholar 

  45. Caillol JP (1994) Comments on the numerical simulations of electrolytes in periodic boundary conditions. J Chem Phys 101:6080–6090

    Article  CAS  Google Scholar 

  46. Smith W (1982) Point multipoles in the Ewald summation. CCP5 Inform Q 4:13–25

    Google Scholar 

  47. Toukmaji A, Sagui C, Board JA, Darden T (2000) Efficient PME-based approach to fixed and induced dipolar interactions. J Chem Phys 113:10913–10927

    Article  CAS  Google Scholar 

  48. Aguado A, Madden P (2003) Ewald summation of electrostatic multipole interactions up to the quadrupolar level. J Chem Phys 119:7471–7483

    Article  CAS  Google Scholar 

  49. Sagui C, Pedersen LG, Darden TA (2004) Towards an accurate representation of electrostatics in classical force fields: efficient implementation of multipolar interactions in biomolecular simulations. J Chem Phys 120:73–87

    Article  PubMed  CAS  Google Scholar 

  50. Smith W (1987) Coping with the pressure: how to calculate the virial. CCP5 Information Quarterly 26:43–50

    Google Scholar 

  51. Alejandre J, Tildesley DJ, Chapela GA (1995) Molecular dynamics simulation of the orthobaric densities and surface tension of water. J Chem Phys 102:4574–4583

    Article  CAS  Google Scholar 

  52. Nose S, Klein M (1983) Constant pressure molecular dynamics for molecular systems. Mol Phys 50:1055–76

    Article  CAS  Google Scholar 

  53. Brown D, Clarke JHR (1991) A loose coupling, constant-pressure, molecular dynamics algorithm for use in the modelling of polymer materials. Comp Phys Comm 62:360–369

    Article  CAS  Google Scholar 

  54. Reif MM, Kraeutler V, Kastenholz MA, Daura X, Huenenberger PH (2009) Molecular dynamics simulations of a reversibly folding beta-Heptapeptide in methanol: influence of the treatment of long-range electrostatic interactions. J Phys Chem B 113:3112–3128

    Article  PubMed  CAS  Google Scholar 

  55. Villarreal MA, Montich GG (2005) On the Ewald artifacts in computer simulations. The test-case of the octaalanine peptide with charged termini. J Biomol Struct Dyn 23:135–142

    CAS  Google Scholar 

  56. Monticelli L, Colombo G (2004) The influence of simulation conditions in molecular dynamics investigations of model beta-sheet peptides. Theo Chem Acc 112:145–157

    Article  CAS  Google Scholar 

  57. Monticelli L, Simões C, Belvisi L, Colombo G (2006) Assessing the influence of electrostatic schemes on molecular dynamics simulations of secondary structure forming peptides. Journal of Physics: condensed Matter 18:S329–S345

    Article  CAS  Google Scholar 

  58. Babin V, Roland C, Darden TA, Sagui C (2006) The free energy landscape of small peptides as obtained from metadynamics with umbrella sampling corrections. J Chem Phys 125:204909

    Article  PubMed  CAS  Google Scholar 

  59. Levy RM, Gallicchio E (1998) Computer simulations with explicit solvent: recent progress in the thermodynamic decomposition of free energies, and in modeling electrostatic effects. Ann Rev Phys Chem 49:531–567

    Article  CAS  Google Scholar 

  60. Hummer G, Pratt LR, Garcia AE (1996) On the free energy of ionic hydration. J Phys Chem 100:1206–1215

    Article  CAS  Google Scholar 

  61. Figuereido F, Buono GSD, Levy RM (1997) On finite-size corrections to the free energy of ionic hydration. J Phys Chem B 101:5622–5623

    Article  Google Scholar 

  62. Hummer G, Pratt LR, Garcia AE (1997) Ion sizes and finite-size corrections for ionic-solvation free energies. J Chem Phys 107:9275–9277

    Article  CAS  Google Scholar 

  63. Sakane S, Ashbaugh HS, Wood RH (1998) Continuum corrections to the polarization and thermodynamic properties of Ewald sum simulations for ions and ion pairs at infinite dimulation. J Phys Chem B 102:5673–5682

    Article  CAS  Google Scholar 

  64. Darden T, Pearlman D, Pedersen L (1998) Ionic charging free energies: spherical versus periodic boundary conditions. J Chem Phys 109:10921–10935

    Article  CAS  Google Scholar 

  65. Herce D, Darden T, Sagui C (2003) Calculation of ionic charging free energies in simulation systems with atomic charges, dipoles and quadrupoles. J Chem Phys 119:7621–7632

    Article  CAS  Google Scholar 

  66. Ferrell R, Bertschinger E (1994) Particle-mesh methods on the connection machine. J Mod Phys 5:933–956

    Google Scholar 

  67. Toukmaji A, Board JA (1996) Ewald sum techniques in perspective: a survey. Comp Phys Comm 95:78–92

    Article  Google Scholar 

  68. Darden T, Toukmaji A, Pedersen L (1997) Long-range electrostatic effects in biomolecular simulations. J Chim Phys 94:1346–1364

    CAS  Google Scholar 

  69. Deserno M, Holm C (1998) How to mesh up Ewald sums i: a theoretical and numerical comparison of various particle mesh routines. J Chem Phys 109:7678–7693

    Article  CAS  Google Scholar 

  70. Sagui C, Darden TA (1999) Molecular dynamics simulations of biomolecules: long-range electrostatic Effects. Annu Rev Biophys Biomol Struct 28:155–179

    Article  PubMed  CAS  Google Scholar 

  71. Sagui C, Darden TA (1999) P3M and PME: a comparison of the two methods. In: Pratt LR, Hummer G (eds) Simulation and theory of electrostatic interactions in solution. AIP, Melville, NY

    Google Scholar 

  72. Case DA, Cheatham TE III, Darden T, Gohlke H, Luo R, Merz KM Jr, Onufriev A, Simmerling C, Wang B, Woods R (2005) The Amber biomolecular simulation programs. J Comput Chem 26:1668–1688

    Article  PubMed  CAS  Google Scholar 

  73. Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) CHARMM: a program for macromolecular energy, minimization and dynamics calculations. J Comp Chem 4:187–217

    Article  CAS  Google Scholar 

  74. Phillips J, Braun R, Wang W, Gumbart J, Tajkhorshid E, Villa E, Chipot C, Skeel R, Kale L, Schulten K (2005) Scalable molecular dynamics with NAMD. J Comp Chem 26:1781–1802

    Article  CAS  Google Scholar 

  75. Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theo Comp 4:435–447

    Article  CAS  Google Scholar 

  76. Bowers KJ, Chow E, Xu H, Dror RO, Eastwood MP, Gregersen BA, Klepeis JL, Kolossvary I, Moraes MA, Sacerdoti FD, Salmon JK, Shan Y, Shaw DE (2006) Scalable algorithms for molecular dynamics simulations on commodity clusters. In: SC ’06: proceedings of the 2006 ACM/IEEE conference on supercomputing. ACM Press

    Google Scholar 

  77. Cerutti DS, Duke RE, Darden TA, Lybrand TP (2009) Staggered mesh Ewald: an extension of the smooth particle-mesh Ewald method adding great versatility. J Chem Theory Comput 5:2322–2338

    Article  PubMed  CAS  Google Scholar 

  78. Chen L, Langdon AB, Birdsall CK (1974) Reduction of grid effects in simulation plasmas. J Comp Phys 14:200–222

    Article  Google Scholar 

  79. Hockney RW, Eastwood JW (1988) Computer simulation using particles. Adam Hilger, Bristol

    Book  Google Scholar 

  80. Cerutti DS, Case DA (2010) Multi-level ewald: a hybrid multigrid/fast Fourier transform approach to the electrostatic particle-mesh problem. J Chem Theory Comput 6:443–458

    Article  PubMed  CAS  Google Scholar 

  81. Duke RE (2006) Amber 9 manual: amber.scripps.edu/doc9/amber9.pdf. AMBER 9, D. A. Case et al., University of California, San Francisco

    Google Scholar 

  82. Schulten K, Phillips JC, Kale LV, Bhatele A (2008) In: Bader D (ed) Petascale computing: algorithms and applications. Chapman & Hall/CRC Press, New York

    Google Scholar 

  83. Brandt A (1977) Multi-level adaptive solutions to boundary value problems. Math Comput 31:333–390

    Article  Google Scholar 

  84. Brandt A (1994) SIAM J Num Anal 31:1695

    Article  Google Scholar 

  85. Brandt A (2001) Multiscale scientific computation: review 2001. In: Barth TJ, Chan TF, Haimes R (eds) Multiscale and multiresolution methods: theory and applications. Springer Verlag, Heidelberg

    Google Scholar 

  86. Beck TL (2000) Real-space mesh techniques in density-functional theory. Rev Mod Phys 72:1041–1080

    Article  CAS  Google Scholar 

  87. Honig B, Nicholls A (1995) Classical electrostatics in biology and chemistry. Science 268:1144–1149

    Article  PubMed  CAS  Google Scholar 

  88. Holst M, Saied F (1993) Multigrid solution of the Poisson-Boltzmann equation. J Comp Chem 14:105–113

    Article  Google Scholar 

  89. Holst M, Kozack RE, Saied F, Subramaniam S (1994) Treatment of electrostatic effects in proteins: multigrid-based Newton iterative method for solution of the full Poisson-Boltzmann equation. Proteins Struct Fun Gen 18:231–241

    Article  CAS  Google Scholar 

  90. Holst M, Saied F (1995) Numerical solution of the nonlinear Poisson-Boltzmann equation: developing more robust and efficient methods. J Comp Chem 16:337–364

    Article  CAS  Google Scholar 

  91. Ripoll DR, Vorobjev YN, Liwo A, Vila JA, Scheraga HA (1996) Coupling between folding and ionization equilibria: effects of pH on the conformational preferences of polypeptides. J Mol Biol 264:770–783

    Article  PubMed  CAS  Google Scholar 

  92. Vorobjev YN, Scheraga HA (1997) A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent. J Comp Chem 18:569–583

    Article  CAS  Google Scholar 

  93. Qian X, Schlick T (2002) Efficient multiple-time-step integrators with distance-based force splitting for particle-mesh-Ewald molecular dynamics simulations. J Chem Phys 116:5971–5983

    Article  CAS  Google Scholar 

  94. Press W, Teukolsky SA, Vettering WT, Flannery BP (1992) Numerical recipes in FORTRAN: the art of scientific computing. Cambridge University Press, Cambridge

    Google Scholar 

  95. Zaslavsky L, Schlick T (1998) An adaptive multigrid technique for evaluating long-range forces in biomolecular simulations. Appl Math Comput 97:237–250

    Article  Google Scholar 

  96. Sagui C, Darden TA (2001) Multigrid methods for classical molecular dynamics simulations of biomolecules. J Chem Phys 114:6578–6591

    Article  CAS  Google Scholar 

  97. Hackbush W (1985) Multigrid methods and applications. Springer, Berlin

    Google Scholar 

  98. Briggs EL, Sullivan DJ, Bernholc J (1996) A real-space multigrid-based approach to large-scale electronic structure calculations. Phys Rev B 54:14362–14375

    Article  CAS  Google Scholar 

  99. Skeel RD, Tezcan I, Hardy DJ (2002) Multiple grid methods for classical molecular dynamics. J Comp Chem 23:673–684

    Article  CAS  Google Scholar 

  100. Goedecker S, Chauvin C (2003) Combining multigrid and wavelet ideas to construct more efficient multiscale algorithms. J Theo Comp Chem 2:483–495

    Article  CAS  Google Scholar 

  101. Izaguirre JA, Hampton SS, Matthey T (2005) Parallel multigrid summation for the N-body problem. J Parall Distrib Comp 65:949–962

    Article  Google Scholar 

  102. Banerjee S, J A Board J (2005) Efficient charge assignment and back interpolation in multigrid methods for molecular dynamics. J Comp Chem 26:957–967

    Google Scholar 

  103. Shan Y, Klepeis JL, Eastwood MP, Dror RO, Shaw DE (2005) Gaussian split Ewald: A fast Ewald mesh method for molecular simulation. J Chem Phys 122:054101

    Article  CAS  Google Scholar 

  104. Groot RD (2003) Electrostatic interactions in dissipative particle dynamics—simulation of polyelectrolytes and anionic surfactants. J Chem Phys 118:11265–11277

    Article  CAS  Google Scholar 

  105. Bishop T, Skeel R, Schulten K (1997) Difficulties with multiple stepping and fast multipole algorithm in molecular dynamics. J Comp Chem 18:1785–91

    Article  CAS  Google Scholar 

  106. Greengard L, Rokhlin V (1987) A fast algorithm for particle simultations. J Comp Phys 73:325–348

    Article  Google Scholar 

  107. Board JA, Causey JW, Leathrum JF, Windemuth A, Schulten K (1992) Accelerated molecular dynamics simulation with the parallel fast multipole algorithm. Chem Phys Lett 198:89–94

    Article  Google Scholar 

  108. Schmidt KE, Lee MA (1991) Implementing the fast multipole method in three dimensions. J Stat Phys 63:1223–1235

    Article  Google Scholar 

  109. Lambert CG, Darden TA, Board JA (1996) A multipole-based method for efficient calculation of forces and potentials in macroscopic periodic assemblies of particles. J Comp Phys 126:274–285

    Article  CAS  Google Scholar 

  110. Figueirido F, Levy R, Zhou R, Berne B (1997) Large scale simulation of macromolecules in solution: combining the periodic fast multipole method with multiple time step integrators. J Chem Phys 106:9835–9849

    Article  CAS  Google Scholar 

  111. Greengard LF (1988) The rapid evaluation of potential fields in particle systems. The MIT Press, Cambridge

    Google Scholar 

  112. Greengard LF (1994) Fast algorithms for classical physics. Science 265:909–914

    Article  PubMed  CAS  Google Scholar 

  113. Greengard L, Rokhlin V (1997) A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica 6:229–270

    Article  Google Scholar 

  114. Greengard L, Rokhlin V (1997) A fast algorithm for particle simulation. J Comput Phys 135:280–292

    Article  Google Scholar 

  115. Cheng H, Greengard L, Rokhlin V (1999) A fast adaptive multipole algorithm in three dimensions. J Chem Phys 155:468–498

    CAS  Google Scholar 

  116. Fenley M, Olson W, Chua K, Boschitsch A (1994) Fast adaptive multipole method for computation of electrostatic energy in simulations of polyelectrolyte DNA. J Comp Chem 17:976

    Article  Google Scholar 

  117. Zhou R, Berne B (1995) A new molecular dynamics method combining the reference system propagator algorithm with a fast multipole method for simulating proteins and other complex systems. J Chem Phys 103:9444–9459

    Article  CAS  Google Scholar 

  118. Ogata S, Campbell T, Kalia R, Nakano A, Vashishta P, Vemparala S (2003) Scalable and portable implementation of the fast multipole method on parallel computers. Comp Phys Comm 153:445–461

    Article  CAS  Google Scholar 

  119. Kurzak J, Pettitt BM (2005) Massively parallel implementation of a fast multipole method for distributed memory machines. J Parall Distrib Comp 65:870–881

    Article  Google Scholar 

  120. Kurzak J, Pettitt BM (2006) Fast multipole methods for particle dynamics. Molecular Simulation 32:775–790

    Article  PubMed  CAS  Google Scholar 

  121. Maggs AC, Rossetto V (2002) Paper1. Phys Rev Lett 88:196402

    Article  PubMed  CAS  Google Scholar 

  122. Alastuey A, Appel W (2000) Physica A 276:508

    Google Scholar 

  123. Rottler J, Maggs AC (2004) Local molecular dynamics with coulombic interactions. Phys Rev Lett 93:170201

    Article  PubMed  CAS  Google Scholar 

  124. Pasichnyk I, Duenweg B (2004) bla. J Phys Cond Mat 16:S3999

    Article  CAS  Google Scholar 

  125. Rottler J (2007) Local electrostatics algorithm for classical molecular dynamics simulations. J Chem Phys 127

    Google Scholar 

  126. Dixon R, Kollman P (1997) Advancing beyond the atom-centered model in additive and non-additive molecular mechanics. J Comp Chem 18:1632–1646

    Article  CAS  Google Scholar 

  127. Wheatley R, Mitchell J (1994) Gaussian multipoles in practice: electrostatic energies for Intermolecular potentials. J Comp Chem 15:1187–1198

    Article  CAS  Google Scholar 

  128. Bayly C, Cieplak P, Cornell W, Kollman P (1993) A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges - the RESP model. J Phys Chem 97:10269–10280

    Article  CAS  Google Scholar 

  129. Francl MM, Chirlian LA (1999) The pluses and minuses of mapping atomic charges to Electrostatic potentials. In: Lipkowitz K, Boyd DB (eds) Reviews in computational chemistry. VCH Publishers, New York

    Google Scholar 

  130. Price S (1999) In: Lipkowitz K, Boyd DB (eds) Reviews in computational chemistry, VCH Publishers, New York

    Google Scholar 

  131. Popelier P (2000) Atoms in molecules: an introduction. Prentice Hall, Harlow

    Google Scholar 

  132. Kosov DS, Popelier PLA (2000) Atomic partitioning of molecular electrostatic potentials. J Phys Chem A 104:7339–7345

    Article  CAS  Google Scholar 

  133. Popelier PLA, Joubert L, Kosov DS (2001) Convergence of the electrostatic interaction based on topological atoms. J Phys Chem A 105:8254–8261

    Article  CAS  Google Scholar 

  134. Popelier PLA, Kosov DS (2001) J Chem Phys 114:6539–6547

    Article  CAS  Google Scholar 

  135. Proft FD, Alsenov CV, Peeters A, Langenaeker W, Geerlings P (2002) Atomic charges, dipole moments and Fukai functions using the Hirshfeld partitioning of the electron density. J Comp Chem 23:1198–1209

    Article  CAS  Google Scholar 

  136. Bader R (1990) Atoms in molecules: a quantum theory. Clarendon Press, Oxford

    Google Scholar 

  137. Sagui C, Pomorski P, Darden TA, Roland C (2004) Ab initio calculation of electrostatic multipoles with Wannier functions for large-scale biomolecular simulations. J Chem Phys 120:4530–4544

    Article  PubMed  CAS  Google Scholar 

  138. Yu H, Hansson T, van Gunsteren WF (2003) Development of a simple, self-consistent polarizable model for liquid water. J Chem Phys 118:221–234

    Article  CAS  Google Scholar 

  139. Lamoureux G, Alexander D MacKerell J, Roux B (2003) A simple polarizable model of water based on classical Drude oscillators. J Chem Phys 119:5185–5197

    Article  CAS  Google Scholar 

  140. Rick SW, Stuart SJ, Berne BJ (1994) Dynamical fluctuating charge force fields: Application to liquid water. J Chem Phys 101:6141–6156

    Article  CAS  Google Scholar 

  141. Ribeiro MCC, Almeida LCJ (1999) Fluctuating charge model for polyatomic ionic systems: a test case with diatomic anions. J Chem Phys 110:11445–11448

    Article  CAS  Google Scholar 

  142. Caldwell J, Dang LX, Kollman PA (1990) Implementation of nonadditive intermolecular potentials by use of molecular dynamics: development of a water-water potential and water-ion cluster interactions. J Am Chem Soc 112:9144–9147

    Article  CAS  Google Scholar 

  143. Ren P, Ponder JW (2003) Polarizable atomic multipole water model for molecular mechanics simulation. J Phys Chem B 107:5933–5947

    Article  CAS  Google Scholar 

  144. Eling D, Darden TA, Woods RJ (2007) Gaussian induced dipole polarization model. J Comp Chem 28:1261–1274

    Article  CAS  Google Scholar 

  145. Ponder JW, Wu C, Ren P, Pande VS, Chodera JD, Schnieders MJ, Haque I, Mobley DL, Lambrecht DS, Robert A DiStasio Jr, Head-Gordon M, Clark GNI, Johnson ME, Head-Gordon T (2010) Current status of the AMOEBA polarizable force field. J Phys Chem B 114:2549–2564

    Article  PubMed  CAS  Google Scholar 

  146. Case DA, Cheatham III TE, Darden TA, Gohlke H, Luo R, Merz KM Jr, Onufirev A, Simmerling C, Wang B, Woods RJ (2005) The Amber biomolecular simulation programs. J Comp Chem 26:1668–1688

    Article  CAS  Google Scholar 

  147. Day PN, Jensen JH, Gordon MS, Webb SP, Stevens WJ, Krauss M, Garmer D, Basch H, Cohen D (1996) An effective fragment method for modeling solvent effects in quantum mechanical calculations. J Chem Phys 105:1968–1986

    Article  CAS  Google Scholar 

  148. Gagliardi L, Lindh R, Karlström G (2004) Local properties of quantum chemical systems: the LoProp approach. J Chem Phys 121:4494–4500

    Article  PubMed  CAS  Google Scholar 

  149. Gresh N, Claverie P, Pullman A (1979) SIBFA. Int J Quantum Chem 253, Symp 11

    Google Scholar 

  150. Anisimov VM, Lamoureux G, Vorobyov IV, Huang N, Roux B, MacKerell AD (2005) Determination of electrostatic parameters for a polarizable force field based on the classical Drude oscillator. J Chem Theory Comput 1:153–168

    Article  CAS  Google Scholar 

  151. Jungwirth P, Tobias D (2002) Ions at the air/water interface. J Phys Chem B 106:6361–6373

    Article  CAS  Google Scholar 

  152. Baucom J, Transue T, Fuentes-Cabrera M, Krahn J, Darden T, Sagui C (2004) Molecular dynamics simulations of the d(CCAACGTTGG)2 decamer in crystal environment: comparison of atomic point-charge, extra-point and polarizable force fields. J Chem Phys 121:6998–7008

    Article  PubMed  CAS  Google Scholar 

  153. Vrbka L, Mucha M, Minofar B, Jungwirth P, Brown E, Tobias D (2004) Propensity of soft ions for the air/water interface. Curr Opin Coll Interface Sci 9:67–73

    Article  CAS  Google Scholar 

  154. Herce D, Perera L, Darden T, Sagui C (2005) Surface solvation for an ion in a water cluster. J Chem Phys 122:024513

    Article  PubMed  CAS  Google Scholar 

  155. Babin V, Baucom J, Darden TA, Sagui C (2006) Molecular dynamics simulations of DNA with polarizable force fields: convergence of an ideal B-DNA structure to the crystallographic structure. J Phys Chem B 110:11571–11581

    Article  PubMed  CAS  Google Scholar 

  156. Harder E, Anisimov VM, Whitfield TW, MacKerell AD, Roux B (2008) Understanding the dielectric properties of liquid amides from a polarizable force field. J Phys Chem B 112:3509–3521

    Article  PubMed  CAS  Google Scholar 

  157. Vladimirov E, Ivanova A, Roesch N (2008) Effect of solvent polarization on the reorganization energy of electron transfer from molecular dynamics simulations. J Chem Phys 129

    Google Scholar 

  158. Harder E, MacKerell AD, Roux B (2009) Many-body polarization effects and the membrane dipole potential. J Am Chem Soc 131:2760+

    Google Scholar 

  159. Vladimirov E, Ivanova A, Roesch N (2009) Solvent reorganization energies in A-DNA, B-DNA, and rhodamine 6G-DNA complexes from molecular dynamics simulations with a polarizable force field. J Phys Chem B 113:4425–4434

    Article  PubMed  CAS  Google Scholar 

  160. Cieplak P, Dupradeau FY, Duan Y, Wang J (2009) Polarization effects in molecular mechanical force fields. J Phys Condens Matter 21

    Google Scholar 

  161. Yan T, Wang Y, Knox C (2010) On the structure of ionic liquids: comparisons between electronically polarizable and nonpolarizable models I. J Phys Chem B 114:6905–6921

    Article  PubMed  CAS  Google Scholar 

  162. Sagui C, Roland C, Pedersen LG, Darden TA (2005) New distributed multipole methods for accurate electrostatics in large-scale biomolecular simulations. In: Leimkuhler B, Chipot C, Elber R, Laaksonen A, Mark A, Schlick T, Schuette C, Skeel R (eds) New algorithms for macromolecular simulations. Springer, Berlin

    Google Scholar 

  163. McMurchie L, Davidson E (1978) One- and two-electron integrals over cartesian Gaussian functions. J Comput Phys 26:218–231

    Article  CAS  Google Scholar 

  164. Ren P, Ponder JW (2002) A consistent treatment of inter- and intramolecular polarization in molecular mechanics calculations. J Comput Chem 23:1497–1506

    Article  PubMed  CAS  Google Scholar 

  165. Ponder JW, Case DA (2003) Force fields for protein simulation. Adv Protein Chem 66:27

    Article  PubMed  CAS  Google Scholar 

  166. Ren P, Ponder JW (2004) Temperature and pressure dependence of the AMOEBA water model. J Phys Chem B 108:13427–13437

    Article  CAS  Google Scholar 

  167. Qian W, Krimm S (2005) Limitations of the molecular multipole expansion treatment of electrostatic interactions for C-H...O and O-H...O hydrogen bonds and application of a general charge density approach. J Phys Chem A 109:5608–5618

    Article  PubMed  CAS  Google Scholar 

  168. Cisneros GA, Piquemal JP, Darden TA (2005) Intermolecular electrostatic energies using density fitting. J Chem Phys 123:044109

    Article  PubMed  CAS  Google Scholar 

  169. Piquemal JP, Gresh N, Giessner-Prettre C (2003) Improved formulas for the calculation of the electrostatic contribution to the intermolecular interaction energy from multipolar expansion of the electronic distribution. J Phys Chem A 107:10353–10359

    Article  CAS  Google Scholar 

  170. Cisneros GA, Tholander SNI, Parisel O, Darden TA, Elking D, Perera L, Piquemal JP (2008) Simple formulas for improved point–charge electrostatics in classical force fields and hybrid quantum mechanical/molecular mechanical embedding. Int J Quantum Chem 108:1905–1912

    Article  PubMed  CAS  Google Scholar 

  171. Freitag MA, Gordon MS, Jensen JH, Stevens WJ (2000) Evaluation of charge penetration between distributed multipolar expansions. J Chem Phys 112:7300–7306

    Article  CAS  Google Scholar 

  172. Wang B, Truhlar DG Including Charge Penetration Effects in Molecular Modeling. J Chem Theo Comp

    Google Scholar 

  173. Volkov A, Koritsanszky T, Coppens P (2004) Combination of the exact potential and multipole methods (EP/MM) for evaluation of intermolecular electrostatic interaction energies with pseudoatom representation of molecular electron densities. Chem Phys Lett 391:170–175

    Article  CAS  Google Scholar 

  174. Volkov A, Li X, Koritsanszky T, Coppens P (2004) Ab initio quality electrostatic atomic and molecular properties including intermolecular energies from a transferable theoretical pseudoatom databank. J Phys Chem A 108:4283–4300

    Article  CAS  Google Scholar 

  175. Volkov A, Coppens P (2004) Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning. J Comp Chem 25:921–934

    Article  CAS  Google Scholar 

  176. Gavezzotti A (2002) Calculation of intermolecular interaction energies by direct numerical integration over electron densities I. Electrostatic and polarization energies in molecular crystals. J Phys Chem B 106:4145–4154

    CAS  Google Scholar 

  177. Piquemal JP, Cisneros GA, Reinhardt P, Gresh N, Darden TA (2006) Towards a force field based on density fitting. J Chem Phys 124:104101

    Article  PubMed  CAS  Google Scholar 

  178. Cisneros GA, Piquemal JP, Darden TA (2006) Generalization of the Gaussian electrostatic model: extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods. J Chem Phys 125:184101

    Article  PubMed  CAS  Google Scholar 

  179. Bagus PS, Hermann K, Bauschlicher CW Jr (1984) A new analysis of charge transfer and polarization for ligand–metal bonding: model studies for Al4CO and Al4NH3. J Chem Phys 80:4378–4386

    Article  CAS  Google Scholar 

  180. Piquemal JP, Marquez A, Parisel O, Giessner-Prettre C (2005) A CSOV study of the difference between HF and DFT intermolecular interaction energy values: the importance of the charge transfer contribution. J Comp Chem 26:1052–1062

    Article  CAS  Google Scholar 

  181. Darden TA (2007) In: Shmueli U (ed) Dual bases in crystallographic computing in international tables of chrystallography. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  182. Cisneros GA, Elking DM, Piquemal JP, Darden TA (2007) Numerical fitting of molecular properties to Hermite Gaussians. J Phys Chem A 111:12049–12056

    Article  PubMed  CAS  Google Scholar 

  183. Elking DM, Cisneros GA, Piquemal JP, Darden TA, Pedersen LG (2010) Gaussian multipole model (GMM). J Chem Theo Comp 6:190–202

    Article  CAS  Google Scholar 

  184. Godbout N, Andzelm J (1998) DGauss Version 2.0, 2.1, 2.3, 4.0: the file that contains the A1 and P1 auxiliary basis sets can be obtained from the CCL WWW site at http://ccl.osc.edu/cca/data/basis-sets/DGauss/basis.v3.html. Computational Chemistry List, Ltd., Ohio

  185. Shaw DE, Maragakis P, Lindorff-Larsen K, Piana S, Dror RO, Eastwood MP, Bank JA, Jumper JM, Salmon JK, Shan Y, Wriggers W (2010) Atomic-level characterization of the structural dynamics of proteins. Science 330:341–346

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgements

This research was supported by NSF under grant FRG-0804549, and by WayneState University.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Celeste Sagui .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this protocol

Cite this protocol

Cisneros, G.A., Babin, V., Sagui, C. (2013). Electrostatics Interactions in Classical Simulations. In: Monticelli, L., Salonen, E. (eds) Biomolecular Simulations. Methods in Molecular Biology, vol 924. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-017-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-62703-017-5_10

  • Published:

  • Publisher Name: Humana Press, Totowa, NJ

  • Print ISBN: 978-1-62703-016-8

  • Online ISBN: 978-1-62703-017-5

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics